Elsevier

Automatica

Volume 44, Issue 5, May 2008, Pages 1233-1239
Automatica

On the coordination of dynamic marketing channels and two-part tariffs

https://doi.org/10.1016/j.automatica.2007.10.009Get rights and content

Abstract

An important result in a static marketing channel is that the manufacturer can reach the vertically integrated channel solution through the use of a two-part wholesale price. This means that the collectively optimal solution is achieved in a decentralized way, i.e., as an equilibrium. This paper investigates under which conditions this result remains valid in a static marketing channel where demand also depends on players’ advertising. Second, it shows that different results are reached when one considers a dynamic marketing channel.

Introduction

Research on conflict and cooperation in marketing channels has been continuously active during the last two decades. The marketing science approach typically adopted a static game theory paradigm with parsimonious models to analyze the interactions between the manufacturer(s) and the retailer(s). One important research question in this stream is whether or not one can induce the different players to coordinate their marketing policies. The motivation here is crystal clear: the lack of coordination in pricing and/or other marketing instruments damages the profitability of the channel and is detrimental to the consumer’s welfare. The optimality of a series of mechanisms, e.g., two-part wholesale tariff, leadership, implicit understanding, cooperative advertising, etc., has been assessed in different institutional and competitive settings (for a survey, see, e.g., Ingene and Parry (2004) and Taboubi and Zaccour (2005)).

One important result, achieved by Jeuland and Shugan (1983) and Moorthy (1987), is that by using a two-part pricing scheme, the manufacturer can coordinate the bilateral-monopoly channel. This means that, with the right pricing policy, one can reproduce, in a decentralized way, the optimal collective results of the vertically integrated channel. These instances, in which the players’ total payoffs are the same under cooperation and noncooperation, are so rare that this result is, by any measure, remarkable. This naturally leads us to question the generality of this result. Ingene and Parry (1995a) showed that it does not extend to the case of one manufacturer serving multiple retailers, because channel coordination is no longer optimal for the manufacturer acting as a Stackelberg leader. Ingene and Parry, 1995b, Ingene and Parry, 2000 further extended their conclusion to a channel formed of asymmetric competing retailers who are treated comparably. Recently, Raju and Zhang (2005) considered a channel with one manufacturer serving a dominant retailer and a fringe. They showed, contrary to Ingene and Parry (1995a), that coordination of the channel through a two-part tariff can be beneficial to the manufacturer.

One common feature of the above-cited papers is that they use a static game model. Although some studies have adopted a differential game formalism to study coordination in marketing channels, they have considered, with the exception of Jørgensen and Zaccour (1999), non-price variables (see, e.g., Chintagunta and Jain (1992) on marketing efforts; Jørgensen, Sigué, and Zaccour (2000), Jørgensen et al., 2001, Jørgensen et al., 2003 on cooperative advertising; Jørgensen, Sigué, and Zaccour (2001) on leadership; Jørgensen, Taboubi, and Zaccour (2006) and Jørgensen and Zaccour (2003) on incentive strategies; and Jørgensen and Zaccour (2004) for a comprehensive survey). The main motivation for using a dynamic setting is that some marketing variables have carry-over effects. For instance, advertising not only affects current sales (a flow), but also feeds the brand goodwill or brand equity (a stock), which in turn has an influence on sales, pricing, etc. Another argument is that partners in marketing channels tend to develop a long-term and evolving relationship. In their seminal paper, Jeuland and Shugan (1983) state that the channel’s actors necessarily face some trade-offs between short- and long-term objectives when attempting to coordinate their efforts, and thus, that a dynamic approach is needed to understand this duality. Note that the idea of a two-part tariff has not, to the best of my knowledge, been considered in a dynamic game context.

The optimality of a two-part tariff has been shown in Jeuland and Shugan (1983) and Moorthy (1987) in a channel where the manufacturer controls the transfer price and the retailer the price to consumer. Since I am interested in considering also advertising, I will then be adding two features to their models, namely players’ advertising efforts, and dynamics. Therefore, I need to separate the two effects, by first verifying whether or not their result can be generalized to static models where the players control–on the top of the transfer and retail prices–other marketing instruments, e.g., advertising. Next, I will adopt a dynamic model which is as close as possible to the static one and verify the generalizability of the results in a static context to a dynamic one. More specifically, my two research questions are:

  • 1.

    Can the result in Jeuland and Shugan (1983) and Moorthy (1987) be extended to a static setting where the players invest in marketing activities, e.g., advertising?

  • 2.

    Can the results obtained in a static game be extended to a dynamic one? 

To answer these questions, I will characterize pricing and advertising strategies for both static and dynamic settings in the following scenarios:

  • 1.

    The vertically integrated channel game. This is the solution that one wishes to achieve in a decentralized manner by implementing a two-part tariff. The game is converted into an optimization problem with the players maximizing the sum of their profits.

  • 2.

    The noncooperative game with two-part tariff. The game is played noncooperatively and a Nash equilibrium is characterized with the manufacturer using a two-part wholesale price policy.

  • 3.

    The commitment game.The assumption is that the manufacturer commits to her strategy in the vertically integrated solution. I verify next if this commitment can be part of a Stackelberg equilibrium.

Comparing the strategies obtained in the first two scenarios will enable me to check if a two-part tariff policy can lead to the solution in the vertically integrated channel. Since, as it will turn out, there are cases where a two-part tariff does not lead to the vertically integrated solution, the last scenario is then put forward to see if a commitment by the manufacturer acting as leader in a Stackelberg game can do the job.

The rest of the paper is organized as follows. In Section 2, I introduce a simple static model of the marketing channel and verify if a two-part tariff leads to channel coordination. In Section 3, I extend the model to a dynamic setting and check if the static results generalize to this context. In Section 4, I briefly conclude.

Section snippets

A simple static channel model

Consider a marketing channel consisting of one manufacturer, player M, and one retailer, player R. Denote by p the retail price, controlled by the retailer, and by w the wholesale price (or transfer price), determined by the manufacturer. Let ai be the advertising (or marketing effort) of player i=M,R. I assume the following simple demand function, Q=β+aM+aRαp, where α>1 and β>0. Note that the above demand function states that the market potential, which is given by β+aM+aR, is not fixed but

A simple dynamic channel model

In order to isolate the effect on the results of introducing dynamics, I shall keep the model as close as possible to the static one.

Suppose that the channel members have an infinite planning horizon, and let t denote time, t[0,). Let aj(t) represent the advertising rate of player j=M,R. As in the static case, I assume that the advertising costs are quadratic and given by CM(aM(t))=(aM(t))22,CR(aR(t))=(aR(t))22. Advertising of both players influence the brand equity, denoted B(t), and assumed

Concluding remarks

Let me first recapitulate the results:

  • 1.

    In a static game, a two-part tariff allows the manufacturer to reach the vertically integrated channel solution when it is not efficient to invest money in marketing effort. When it is worth it to do so, one needs an additional condition to obtain the VI solution in a decentralized way, namely that the manufacturer acts as a leader and announces first that she will implement her part of the cooperative solution. This commitment is credible since that this

Georges Zaccour holds the Chair in Game Theory and Management and is full professor of Marketing at HEC Montrèal. He holds a Ph.D. in Management Science, an M.Sc. in International Business from HEC Montréal and a licence in Mathematics and Economics from Université Paris-Dauphine. He served as Director of GERAD, an interuniversity research center and Director of Marketing Department and Ph.D. program at HEC Montréal. His research areas are differential games, optimal control and operations

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Georges Zaccour holds the Chair in Game Theory and Management and is full professor of Marketing at HEC Montrèal. He holds a Ph.D. in Management Science, an M.Sc. in International Business from HEC Montréal and a licence in Mathematics and Economics from Université Paris-Dauphine. He served as Director of GERAD, an interuniversity research center and Director of Marketing Department and Ph.D. program at HEC Montréal. His research areas are differential games, optimal control and operations research applied to marketing, energy sector and environmental management, areas in which he has published more than eighty five papers and co-edited thirteen volumes. He coauthors the book Differential Games in Marketing. His research is regularly funded by the Natural Sciences and Engineering Research Council of Canada. He is Associate Editor of the International Game Theory Review, Environmental Modeling & Assessment, Computational Management Science and Journal of Operations & Logistics. He is fellow of The Royal Society of Canada and was President of the International Society of Dynamic Games (2002–2006).

I would like to thank the three anonymous Reviewers for their very helpful comments. I also thank Guiomar Martín-Herrán for her comments on different versions of this paper and Sihem Taboubi and Simon-Pierre Sigué for their comments on an earlier version. Research supported by NSERC Canada and started when I was visiting professor at Universidad de Valladolid, Spain, under grant SAB2004-0162. This paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Editor Berç Rüstem.

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